The AKG C414 B-ULS is a good choice, due to the lack of a presence peak in the treble response--it's a very neutral sounding mike that way, and so will work well on a variety of instruments. Mikes with treble presence peaks may sound nice on some instruments and not so good on others.
Budget choice: the AKG C1000-S can sound good on strings if you use the super-cardioid adapter, which tends to flatten out the top end response. (Without the adapter--in cardioid mode--the C1000-S sounds rather bright, which can be a problem with some string instruments.)
Regarding instrument-mounted mikes, I have often used a Countryman Isomax cardioid lavalier mike for recording jazz acoustic bass, clipping the mike to the low "E" string, just below the bridge. This particular setup sounds quite natural and gives me more isolation than standard mikes on stands. If I don't need the isolation, the Neumann U87 (or U67 if it's available) sounds great on acoustic bass.